Seiji Mizuno

We investigate resonant localization and reflection-phase dynamics in graded phononic superlattices with spatially varying band edges. Starting from the elastic wave equation, we derive, using the local periodic approximation and the multiple-scale method, an effective Schr\"odinger-type equation for the envelope function, whose coefficients are expressed in terms of unit-cell averages involving the local Bloch mode. Spatial modulation of the local band edge then acts as an effective potential containing an internal turning point, allowing the system to be interpreted as an open quasibound scattering structure. For parabolic band-edge profiles, the effective potential becomes approximately harmonic and supports a series of quasibound resonances with a half-harmonic-like character. We show that the resonance frequencies form a nearly equally spaced series consistent with WKB quantization, and that the spatial mode profiles are accurately described by Hermite-function envelopes. The turning-point region is described by an Airy-function connection that consistently links the oscillatory and evanescent regions of the wave field. We further show that the semiclassical round-trip phase determines the quasibound resonance condition, while the Wigner reflection delay, defined from the total scattering phase, exhibits pronounced peaks near these resonances. These results establish a semiclassical description of resonant localization, quasibound scattering, and temporal delay in graded periodic wave systems.

We investigate a one-dimensional AB superlattice in which the thickness of the B layer is monotonically graded, and analyze the frequency-selective localization and time-delay characteristics of elastic waves associated with phononic rainbow trapping. Using the transfer-matrix method, we demonstrate a position-dependent shift of the local band gaps and the emergence of a broadband high-reflection band. By evaluating the reflection phase time from the frequency derivative of the complex reflection phase, we clarify the correspondence between discrete standing-wave modes formed in an effective cavity created by the grading and the peaks of the phase time. Furthermore, simulations of monochromatic-wave responses and the time evolution of Gaussian wave packets visualize long-time trapping near the barrier at the back side of the structure and the associated increase in reflection time. These results show that the interplay among the spatial slope of the local band gaps, the reflection position, and the effective mode condition determines the broadband energy-trapping and time-delay characteristics, and provide design guidelines for phononic metamaterials such as broadband sound-absorbing structures and vibration energy-harvesting devices.

We analytically studied the Fano resonance in a simple coupled oscillator system. We demonstrate directly from the equation of motion that the resonance profile observed in this system is generally described by the Fano formula with a complex Fano parameter. The analytical expressions are derived for resonance frequency, resonance width, and Fano parameter, moreover conditions under which the Fano parameter becomes a real number are also examined. These expressions, derived for the simple system, are expected to be helpful for considering various other physical systems because the Fano resonance is a general wave phenomenon.

We theoretically study the phonons propagating through a superlattice consisting of alternating layers of an elastic solid and a fluid. In this structure, there exist phononic bandgaps not originating from Bragg reflections. We examine the origin of these non-Bragg gaps and show that they are peculiar to the solid–fluid superlattices, where the number of allowed modes varies periodically. Even a single solid layer immersed in fluid contains discrete frequencies at which incident waves are perfectly reflected. We demonstrate the resonant reflection process at these frequencies. In the multilayered structure, these transmission zeros are gathered and form a bandgap. This is similar to the relation between atomic levels and an electronic energy band, though the allowed and forbidden states are interchanged. This non-Bragg gap introduces novel degrees of freedom to the design of phononic bandgap structures.

We study numerically the phonon dispersion relations and corresponding displacement fields for a circular cross-section nanowire superlattices consisting of anisotropic GaN and AlN. We determine a set of parameters which gives complete phononic bandgaps. The results suggest the potential for manipulating phonons in the micro/nano electromechanical systems.

We study theoretically the phonon modes in a square cross‐section nanowire superlattice (NWSL) consisting of InAs and InP. The phonon modes in the NWSL composed of cubic materials are classified into five types, i.e., A₁, A₂, B₁, B₂, and E modes. We calculate the dispersion relations of each phonon mode and corresponding displacement fields for this NWSL. The A₁, A₂, B₁, B₂, and E modes have features of dilatational, torsional, stretching, shear, and flexural modes, respectively. We examine the effects of both the superlattice modulation along the wire axis and lateral confinement of phonons.